A model rocket is launched from the ground with an initial velocity of 60 feet per second. the function g (t) = - 16t^2 + 60t represents the height of the rocket, g (t), t seconds after it was launched ... what is the absoloute max, zeros, domain, and range

If we use our trusty ti's this will be a breeze

domain is the numbers we can use

obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3, pi ...)

zeroes is when you set absolute max using ti is

remember vertex form which is

max height of something in

ax^2+bx+c form is - b/2a

-16t^2+60t+0

a=-16

b=60

-60 / (2 times - 16)

-60/-32=30/16=15/8=1 and 7/8 so subsitute for t

g (15/8) = - 16 (15/8) ^2+60 (15/8) = 225/4=56.25=max height

zeroes is when the equation equals 0

so set it to zero

0=-16t^2+60t

factor

0 = (-4t) (4x-15)

set each to zero

-4x=0

x=0

4x-15=0

add 15

4x=15

divid 4

x=15/4

so the zeros are t=0 and t=15/4

domain is all the nuumbers that can be used logically for time

logically, we cannot have negative time, so all real positive

[0,∞)

(that means from 0 to infinity includng 0 so 0 < t<∞))

range is the output

output=height

we find the min height and max height

min=0

max=56.25

so range=0 to 56.25 or

[0,56.25]

max height=56.25 ft (15/8 seconds)

zeroes=0 sec and 15/4 sec

domain=all real positive numbers including zero or [0, ∞)

range=[0,56.25]